TSTP Solution File: SET073-7 by Faust---1.0
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%------------------------------------------------------------------------------
% File : Faust---1.0
% Problem : SET073-7 : TPTP v3.4.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : faust %s
% Computer : art01.cs.miami.edu
% Model : i686 i686
% CPU : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory : 1003MB
% OS : Linux 2.6.17-1.2142_FC4
% CPULimit : 600s
% DateTime : Wed May 6 15:27:07 EDT 2009
% Result : Unsatisfiable 0.3s
% Output : Refutation 0.3s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 15 ( 9 unt; 0 def)
% Number of atoms : 23 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 3 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Faust---1.0 format not known, defaulting to TPTP
fof(prove_corollary_to_unordered_pair_axiom1_1,plain,
member(x,universal_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(164972368,plain,
member(x,universal_class),
inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_1]),
[] ).
fof(unordered_pair2,plain,
! [A,B] :
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(163917592,plain,
( ~ member(A,universal_class)
| member(A,unordered_pair(A,B)) ),
inference(rewrite,[status(thm)],[unordered_pair2]),
[] ).
fof(existence_of_null_class,plain,
! [A] : ~ member(A,null_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(164849872,plain,
~ member(A,null_class),
inference(rewrite,[status(thm)],[existence_of_null_class]),
[] ).
fof(subclass_members,plain,
! [A,B,C] :
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(163835456,plain,
( ~ subclass(A,B)
| ~ member(C,A)
| member(C,B) ),
inference(rewrite,[status(thm)],[subclass_members]),
[] ).
fof(equal_implies_subclass2,plain,
! [B,A] :
( ~ $equal(B,A)
| subclass(B,A) ),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(163887464,plain,
( ~ $equal(B,A)
| subclass(B,A) ),
inference(rewrite,[status(thm)],[equal_implies_subclass2]),
[] ).
fof(prove_corollary_to_unordered_pair_axiom1_2,plain,
$equal(unordered_pair(x,y),null_class),
file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),
[] ).
cnf(164976104,plain,
$equal(unordered_pair(x,y),null_class),
inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_2]),
[] ).
cnf(177294640,plain,
subclass(unordered_pair(x,y),null_class),
inference(resolution,[status(thm)],[163887464,164976104]),
[] ).
cnf(179975728,plain,
~ member(A,unordered_pair(x,y)),
inference(forward_subsumption_resolution__resolution,[status(thm)],[164849872,163835456,177294640]),
[] ).
cnf(contradiction,plain,
$false,
inference(forward_subsumption_resolution__resolution,[status(thm)],[164972368,163917592,179975728]),
[] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% Proof found in: 1 seconds
% START OF PROOF SEQUENCE
% fof(prove_corollary_to_unordered_pair_axiom1_1,plain,(member(x,universal_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(164972368,plain,(member(x,universal_class)),inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_1]),[]).
%
% fof(unordered_pair2,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(163917592,plain,(~member(A,universal_class)|member(A,unordered_pair(A,B))),inference(rewrite,[status(thm)],[unordered_pair2]),[]).
%
% fof(existence_of_null_class,plain,(~member(A,null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(164849872,plain,(~member(A,null_class)),inference(rewrite,[status(thm)],[existence_of_null_class]),[]).
%
% fof(subclass_members,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(163835456,plain,(~subclass(A,B)|~member(C,A)|member(C,B)),inference(rewrite,[status(thm)],[subclass_members]),[]).
%
% fof(equal_implies_subclass2,plain,(~$equal(B,A)|subclass(B,A)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(163887464,plain,(~$equal(B,A)|subclass(B,A)),inference(rewrite,[status(thm)],[equal_implies_subclass2]),[]).
%
% fof(prove_corollary_to_unordered_pair_axiom1_2,plain,($equal(unordered_pair(x,y),null_class)),file('/home/graph/tptp/TSTP/PreparedTPTP/tptp---none/SET/SET073-7.tptp',unknown),[]).
%
% cnf(164976104,plain,($equal(unordered_pair(x,y),null_class)),inference(rewrite,[status(thm)],[prove_corollary_to_unordered_pair_axiom1_2]),[]).
%
% cnf(177294640,plain,(subclass(unordered_pair(x,y),null_class)),inference(resolution,[status(thm)],[163887464,164976104]),[]).
%
% cnf(179975728,plain,(~member(A,unordered_pair(x,y))),inference(forward_subsumption_resolution__resolution,[status(thm)],[164849872,163835456,177294640]),[]).
%
% cnf(contradiction,plain,$false,inference(forward_subsumption_resolution__resolution,[status(thm)],[164972368,163917592,179975728]),[]).
%
% END OF PROOF SEQUENCE
%
%------------------------------------------------------------------------------